p-adic heights of generalized Heegner cycles

Ariel Shnidman

doi:10.5802/aif.3033

p-adic heights of generalized Heegner cycles

Ariel Shnidman^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

We relate the p-adic heights of generalized Heegner cycles to the derivative of a p-adic L-function attached to a pair (f, χ), where f is an ordinary weight 2r newform and χ is an unramified imaginary quadratic Hecke character of infinity type (ℓ, 0), with 0 < ℓ < 2r. This generalizes the p-adic Gross-Zagier formula in the case ℓ = 0 due to Perrin-Riou (in weight two) and Nekovář (in higher weight).

Original language	English
Pages (from-to)	1117-1174
Number of pages	58
Journal	Annales de l'Institut Fourier
Volume	66
Issue number	3
DOIs	https://doi.org/10.5802/aif.3033
State	Published - 2016
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2016, Association des Annales de l'Institut Fourier. All rights reserved.

Keywords

Algebraic cycles
Modular forms
p-adic L-functions

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10.5802/aif.3033

Cite this

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abstract = "We relate the p-adic heights of generalized Heegner cycles to the derivative of a p-adic L-function attached to a pair (f, χ), where f is an ordinary weight 2r newform and χ is an unramified imaginary quadratic Hecke character of infinity type (ℓ, 0), with 0 < ℓ < 2r. This generalizes the p-adic Gross-Zagier formula in the case ℓ = 0 due to Perrin-Riou (in weight two) and Nekov{\'a}{\v r} (in higher weight).",

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AB - We relate the p-adic heights of generalized Heegner cycles to the derivative of a p-adic L-function attached to a pair (f, χ), where f is an ordinary weight 2r newform and χ is an unramified imaginary quadratic Hecke character of infinity type (ℓ, 0), with 0 < ℓ < 2r. This generalizes the p-adic Gross-Zagier formula in the case ℓ = 0 due to Perrin-Riou (in weight two) and Nekovář (in higher weight).

KW - Algebraic cycles

KW - Modular forms

KW - p-adic L-functions

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JF - Annales de l'Institut Fourier

IS - 3

ER -

p-adic heights of generalized Heegner cycles

Abstract

Bibliographical note

Keywords

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